Constraint the camera to look at an object
Set the camera with a Track To constraint.


Select the "Target" object.
In the "To" section select -Z and in the "Up" section set it to Y 
Use World Space








The camera will then point at the target object's origin.

To understand those settings you have to think of the LOCAL AXES for the camera: X is Horizontal, Y vertical and Z is depth. Negative Z is what is in front of the camera.



To maintain the object's Z axis aligned at all times enable Target Z.